The underlying technology of ReFS features a number of improvements over NTFS. While these changes should be invisible to the average user, the performance and resiliency improvements should be obvious in certain circumstances.
One of the changes is switching from journaling to write-on-allocate for metadata updates. In NTFS, when metadata for a file or folder (name, security permissions, and other information) is altered, those changes are also recorded in a journal in case they need to be rolled back. Normally this is reliable, but data may be corrupted if the drive loses power in the middle of an operation.
The write-on-allocate strategy used in ReFS improves on that by making all metadata changes to a different location (ie copying, rather than overwriting) so the original metadata is left completely intact. If the drive loses power while metadata is being changed, the original will still be available.
You can take that a step further by enabling integrity streams, which is designed for optimum corruption resistance. With this feature enabled, both files and the associated metadata are written to a new location on the disk. The original is maintained in case you need to recover it later.
While integrity streams should be better from a reliability standpoing, it may degrade performance of certain applications. Databases, in particular, may take a performance hit when data is moved around the disc too much. Of course, if your database isn't changed often, this may not be a consideration.
With a feature called integrity streams, the same strategy can be used for modifying the actual file data. In other words, if you edit and save a file, rather than being overwritten a new version of the file will be created. Once it is saved, the new (and updated) copy replaces the original.
ReFS also uses B+ trees for mapping out file and folder names and locations. This essentially removes the NTFS limits on file and folder size and the number of characters in a name. There are still limits, but they are literally thousands of times the size of the biggest consumer hard drives available today.
Drives formatted with the ReFS file system may also use another new feature in Windows 8 called Storage Spaces (also available for NTFS drives). Storage Spaces provides various options for pooling physical discs into a single logical location. This replaces the striping, mirroring, and spanning features from previous Windows versions.
Since a big part of ReFS comes directly from NTFS, the file system API is the same. That means programs which work with the NTFS file system should work exactly the same with ReFS. Actually there will be minor differences, but those are due to features which have been removed either because they had already been replaced or Microsoft felt no one used them.
The NTFS features not found in ReFS are named streams, object IDs, short names, compression, EFS (Encryption File System), user data transactions, sparse, hard-links, extended attributes, and quotas.
If there's one thing likely to annoy some people about ReFS, it's the lack of a drive conversion option. The only way to convert from NTFS to ReFS is to copy the drive contents to a second drive, format the original with ReFS, and then copy the data back.
You can find more technical information on the Building Windows 8 blog.